Limited lookahead has been studied for decades in perfect-information games. We initiate a new direction via two simultaneous deviation points: generalization to imperfect-information games and a game-theoretic approach. We study how one should act when facing an opponent whose lookahead is limited. We study this for opponents that differ based on their lookahead depth, based on whether they, too, have imperfect information, and based on how they break ties. We characterize the hardness of finding a Nash equilibrium or an optimal commitment strategy for either player, showing that in some of these variations the problem can be solved in polynomial time while in others it is PPAD-hard, NP-hard, or inapproximable. We proceed to design algorithms for computing optimal commitment strategies---for when the opponent breaks ties favorably, according to a fixed rule, or adversarially. We then experimentally investigate the impact of limited lookahead. The limited-lookahead player often obtains the value of the game if she knows the expected values of nodes in the game tree for some equilibrium---but we prove this is not sufficient in general. Finally, we study the impact of noise in those estimates and different lookahead depths.

中文翻译：

---

不完美信息游戏中的有限前瞻

在完美信息博弈中，有限的前瞻已经研究了几十年。我们通过两个同时发生的偏差点启动了一个新方向：对不完美信息游戏的泛化和博弈论方法。我们研究当面对一个前瞻有限的对手时应该如何行动。我们针对不同的对手研究这一点，这些对手根据他们的前瞻深度、他们是否也有不完善的信息以及他们如何打破平局而有所不同。我们描述了为任一参与者寻找纳什均衡或最佳承诺策略的难度，表明在这些变体中的一些变体中，问题可以在多项式时间内解决，而在其他变体中，它是 PPAD-hard、NP-hard 或不可近似的。我们继续设计算法来计算最优承诺策略——当对手有利地打破平局时，根据固定规则或对抗性。然后我们通过实验研究有限前瞻的影响。如果有限前瞻玩家知道博弈树中节点的期望值以达到某种平衡，她通常会获得博弈的价值——但我们证明这通常是不够的。最后，我们研究了这些估计中噪声的影响和不同的前瞻深度。